Question: Calculating Surface Area of Prisms and Pyramids Using Nets What is the surface area of the given triangular prism with an isosceles base? In the triangular prism: BC = 6 ft AD = 5 ft FH = 5.83 ft CH = 9 ft Use the given information to complete the worksheet. Let's figure out a solution plan. How many shapes of different dimensions make up the net of this figure? 3 Shape Legend Base Length (ft) Height Length (ft) Area of a Single Shape (ft²) How Many of This Shape Total Area of These Shapes (ft²) Triangle Rectangle Rectangle The surface area of the triangular prism with an isosceles base is

1. **State the problem:** We need to find the surface area of a triangular prism with an isosceles triangular base. 2. **Identify the shapes in the net:** The net consists of 3 rectangles and 2 congruent triangles. 3. **Given dimensions:** - Base of triangle (BC) = $6$ ft - Height of triangle (AD) = $5$ ft - Slant height of triangle side (FH) = $5.83$ ft - Length of prism (CH) = $9$ ft 4. **Calculate the area of one triangle:** $$\text{Area}_{\triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 5 = 15 \text{ ft}^2$$ 5. **Calculate the area of the rectangles:** - Rectangle 1 (base rectangle): length $6$ ft, height $9$ ft $$\text{Area}_{R1} = 6 \times 9 = 54 \text{ ft}^2$$ - Rectangle 2 (side rectangle): length $5$ ft, height $9$ ft $$\text{Area}_{R2} = 5 \times 9 = 45 \text{ ft}^2$$ - Rectangle 3 (slant side rectangle): length $5.83$ ft, height $9$ ft $$\text{Area}_{R3} = 5.83 \times 9 = 52.47 \text{ ft}^2$$ 6. **Calculate total area of triangles:** There are 2 congruent triangles: $$2 \times 15 = 30 \text{ ft}^2$$ 7. **Calculate total area of rectangles:** $$54 + 45 + 52.47 = 151.47 \text{ ft}^2$$ 8. **Calculate total surface area:** $$\text{Surface Area} = \text{Area of triangles} + \text{Area of rectangles} = 30 + 151.47 = 181.47 \text{ ft}^2$$ **Final answer:** The surface area of the triangular prism is approximately $181.47$ square feet.